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Abstract

When two entangled qubits, each owned by Alice and Bob, undergo separate decoherence, the amount of entanglement is reduced, and often, weak decoherence causes complete loss of entanglement, known as entanglement sudden death. Here we show that it is possible to apply quantum measurement reversal on a single-qubit to avoid entanglement sudden death, rather than on both qubits. Our scheme has important applications in quantum information processing protocols based on distributed or stored entangled qubits as they are subject to decoherence.

Figures (8)

Fig. 1 (a) Decoherence suppression scheme using quantum measurement reversal for a single qubit state. To suppress decoherence, a set of weak and reversing measurements are performed before and after decoherence, respectively. Note that the size of the spheres corresponds to the population fraction of each level, |0〉 and |1〉. (b) Entanglement of two-qubit states which undergo separate decoherence can be recovered if both Alice and Bob carry out quantum measurement reversal. (c) The situation we considered here: Only Alice performs single-qubit quantum measurement reversal on her subsystem. W : weak measurement, D: decoherence, R: reversing measurement, Sys: system, Env: environment.

Fig. 2 (a) Alice and Bob initially share a pure entangled state |Φ〉. When both subsystems suffer from decoherence, the final state ρD loses its entanglement partially or completely. (b) To suppress decoherence, Alice performs a set of weak measurement WA (p) and reversing measurement RA (pr) before and after her subsystem undergoes decoherence, respectively. Then, the resulting state ρA becomes closer to the initial state |Φ〉, i.e. ρA is more entangled than ρD. Note that Bob is not involved in this decoherence suppression scheme.

Fig. 4 (a) Concurrence CD of the resulting state ρD decreases as the strength of the decoherence (D) increases. (b) Concurrence CA (CB) of the final state ρA (ρB) in the case that only Alice (Bob) perfroms single-qubit quantum measurement reversal on her (his) qubit (DA = DB = 0.617). p is the strength of the weak measurement. Solid lines are theoretical results. Negative values corresponds to ΛD for (a), and ΛA and ΛB for (b), respectively. Note that C = 0 when Λ< 0 since C = max {0,Λ}. We evaluated the fidelity between the ideally expected state and the experimentally reconstructed state for ρA and ρB. The fidelity values for ρA (FA) and ρB (FB) are averaged from the experimental data of (b), and we obtain FA = 0.945 ± 0.024 and FB = 0.935 ± 0.028.

Fig. 5 Result of the scenario in Fig. 1(a) with D = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. Ffix and Fexp increase as the weak measurement strength p increases. (b) Success probabilities
PSfix and
PSexp as functions of |α| and p.
PSexp is always larger than
PSfix regardless of |α| and p values. Note that F → 1 and PS → 0 as p → 1 for both cases of
prfix and
prexp .

Fig. 6 Result of the scenario in Fig. 1(b) with DA = DB = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. The state fidelities increase as the weak measurement strength p increases. (b) Success probabilities
PSfix and
PSexp as functions of |α| and p. Note that PS → 0 as p → 1 for all both cases.

Fig. 7 Result of the scenario in Fig. 1(c) with DA = DB = 0.617. (a) State fidelities Ffix and Fexp as functions of |α| and p. The state fidelities increase as the weak measurement strength p increases. (b) Success probabilities
PSfix and
PSexp as functions of |α| and p.
PSfix is always larger than
PSexp regardless of |α| and p values. Note that F does not approach to unity and PS → 0 as p → 1 for both cases of
prfix and
prexp.

Fig. 8 Result of the scenario in Fig. 1(c) with DA = 0.617 and DB = 0. (a) State fidelities Ffix and Fexp as functions of |α| and p. (b) Success probabilities
PSfix and
PSexp as functions of |α| and p.
PSexp is always larger than
PSfix regardless of |α| and p values. Note that F → 1 and PS → 0 as p → 1 for both cases of
prfix and
prexp.